Finite Group Databasebeta

← #14672465

Subgroups — #14672465

Order 2816.

396 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073803C211yesmaximal, characteristic
2#13068612C211yesmaximal, characteristic
3#13066742C212yesmaximal
4#13066742C212yesmaximal
5C4×C11×#101C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66923C411yescharacteristic
8C2×C11×#101C2212yes—
9C4×C11×M16—21no—
10#10622843C2211yescharacteristic
11#10622843C2211yescharacteristic
12C2×#66900C2212yes—
13#10622597—21no—
14#10622597—21no—
15#10622590C411yescharacteristic
16#10622589C411yescharacteristic
17C4×C4⋊Dic11C411yescharacteristic
18#10622546—21no—
19#10622546—21no—
20#10622537—21no—
21C11×#343—21no—
22#10622168—21no—
23C22×Q8×C11C2311yescharacteristic
24C2×C11×M16—22no—
25C4×Q8×C11—41no—
26C4×Q8×C11—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4D411yescharacteristic
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11C2×C411yescharacteristic
35C2×C4⋊Dic11C2×C411yescharacteristic
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×C4×Dic11C2×C411yescharacteristic
41C2×C4×Dic11C2×C411yescharacteristic
42C2×#4318—22no—
43#66923—41no—
44#66923—41no—
45C11×#101—22no—
46C11×#101Q814yes—
47C11×#97—41no—
48C4×C8×C11—41no—
49#66900—24no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C4⋊(C11⋊C8)—41no—
58C4⋊(C11⋊C8)—41no—
59#13303—111nomaximal, Sylow
60C2×Q8×C11—41no—
61C2×Q8×C11—41no—
62C2×Q8×C11C2×Q812yes—
63C2×Q8×C11#4112yes—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C11×M16—24no—
76C11×M16—42no—
77C2×C8×C11—42no—
78C11×C4⋊C4—41no—
79C11×C4⋊C4—41no—
80C11×C4⋊C4—41no—
81C42×C11—21no—
82C42×C11—21no—
83C42×C11—21no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89C4⋊Dic11—42no—
90Dic11⋊C4—42no—
91Dic11⋊C4—42no—
92Dic11⋊C4—42no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95C4×Dic11—41no—
96C4×Dic11—41no—
97#4318—42no—
98#4318—42no—
99C2×C11⋊C8—42no—
100#2565—111no—
101#1801—111no—
102C4×#101D1111yescharacteristic
103#1394—112no—
104#1394—112no—
105C23×C11C2×C22⋊C411yescharacteristic
106Q8×C11—42no—
107Q8×C11—42no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11#9911yescharacteristic
122C2×C4×C11#9911yescharacteristic
123C2×C4×C11C4×Q812yes—
124C2×C4×C11C22⋊Q812yes—
125C2×C4×C11#12411yescharacteristic
126C2×C4×C11C4⋊Q811yescharacteristic
127C2×Dic11—22no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—42no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C8×C11—44no—
139C11⋊C8—82no—
140C2×#125—111no—
141C2×C4×Q8C2×D1111yescharacteristic
142#423—221no—
143C2×#101—112no—
144C2×#101C2×D1112yes—
145C4×M16—21no—
146#398—221no—
147#398—221no—
148#391—111no—
149#391—111no—
150#387—221no—
151#387—221no—
152#384—111no—
153#382—111no—
154C4×C4⋊C4—111no—
155#343—21no—
156#343—221no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11#39111yescharacteristic
160C22×C11C2×#9911yescharacteristic
161C22×C11#41011yescharacteristic
162C4×C11—21no—
163C4×C11—21no—
164C4×C11—22no—
165C4×C11—22no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171Dic11—42no—
172Dic11—81no—
173Dic11—81no—
174Dic11—81no—
175C22×Q8C22×D1111yescharacteristic
176C2×M16—22no—
177C2×M16—222no—
178#125—441no—
179#125—441no—
180C4×Q8—41no—
181C4×Q8—41no—
182C2×C4⋊C4—111no—
183C2×C4⋊C4—111no—
184C2×C4⋊C4—221no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4C4×D1111yescharacteristic
190C2×C4⋊C4D4411yescharacteristic
191C2×C4⋊C4C22⋊D1111yescharacteristic
192C2×C42—111no—
193C2×C42—111no—
194C2×C42C4×D1111yescharacteristic
195C2×C42D4411yescharacteristic
196C2×C42C22⋊D1111yescharacteristic
197C4⋊C8—441no—
198C4⋊C8—441no—
199#101—22no—
200#101—224no—
201#101Dic2214yes—
202#97—41no—
203C4×C8—41no—
204#95—221no—
205#95—221no—
206#95—221no—
207#95—221no—
208#95—221no—
209#95—221no—
210#95—221no—
211C2×C11—21no—
212C2×C11—21no—
213C2×C11#199611yescharacteristic
214C2×C11#213211yescharacteristic
215C2×C11#213311yescharacteristic
216C2×Q8—41no—
217C2×Q8—41no—
218C2×Q8C2×Dic2212yes—
219C2×Q8#433912yes—
220C22×C4—221no—
221C22×C4—221no—
222C22×C4—221no—
223C22×C4—221no—
224C22×C4(C2×D11)⋊C411yescharacteristic
225C22×C4(C2×D11)⋊C411yescharacteristic
226C22×C4(C2×D11)⋊C411yescharacteristic
227C22×C4(C2×D11)⋊C411yescharacteristic
228C22×C4C2×C4×D1111yescharacteristic
229C22×C4C2×D4411yescharacteristic
230C22×C4C2×C22⋊D1111yescharacteristic
231M16—24no—
232M16—42no—
233M16—442no—
234M16—442no—
235C2×C8—42no—
236C2×C8—442no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—441no—
241C4⋊C4—441no—
242C4⋊C4—442no—
243C4⋊C4—442no—
244C4⋊C4—442no—
245C4⋊C4—442no—
246C4⋊C4—441no—
247C4⋊C4—441no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—441no—
255C42—441no—
256C11#1330311yescharacteristic, complemented, Sylow
257C23C2×(C2×D11)⋊C411yescharacteristic
258Q8—42no—
259Q8—42no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—222no—
274C2×C4—441no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4—442no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4#6687011yescharacteristic
285C2×C4#6687011yescharacteristic
286C2×C4C4×Dic2212yes—
287C2×C4#6692211yescharacteristic
288C2×C4#6692811yescharacteristic
289C2×C4#6697712yes—
290C8—44no—
291C8—882no—
292C22—21no—
293C22—21no—
294C22#1062254211yescharacteristic
295C22C2×#6687011yescharacteristic
296C22#1062261911yescharacteristic
297C4—22no—
298C4—21no—
299C4—22no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—442no—
307C4—881no—
308C4—881no—
309C4—881no—
310C2—21no—
311C2—21no—
312C2#1306960111yescharacteristic
313C2#1307029911yescharacteristic
314C2#1307030311yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC4×C11×#101C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC22×Q8×C11C23
hypercenterC4×#101D11
hypocenterC11#13303
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
256. C11#13303semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130738032
#130686122
#130667422
C4×C11×#1012
#1330311